The 2017 report card for America's Infrastructure by American Society of Infrastructure (ASCE) [1], reports that one in eleven of the nation's bridges are rated as structurally deficient and the average age of the nation's 614,387 bridges is 43 years. Also the Federal Highway Administration (FHWA) calculated that more than 39% of existing bridges have exceeded their 50-year design life and an additional 15% are between the ages of 40 and 49. Thus, the need for structural health monitoring of bridges in terms of maintenance, repair and rehabilitation is becoming very critical. Pile foundations are the most common type of deep foundations for bridges and are used for various conditions such as loose soil, large loads from structure, lack of space for shallow foundation. The capacity of a pile foundation is directly related to the embedded length. Reduction in the effective depth of the foundation especially due to scour may cause significant reduction in strength and thus compromises the safety of the structure. Hence it is beneficial to evaluate the effective embedded length of pile using nondestructive testing (NDT). There have been multiple NDT methods [2] developed for quality assurance of newly constructed pile foundations and evaluation of an existing foundation.
The terms nondestructive testing/nondestructive evaluation were first used in the context of pile foundations in the 1970's and can be traced back to two the work of Levy [3] and Davis and Dunn [4]. Levy described a mechanism used to test the condition of cast in-situ concrete piles using a sonic pulse transmitter and receiver. Davis and Dunn used electrodynamic vibrator placed on the head of the pile to produce sinusoidal waves of varied frequencies and the response was recorded using a transducer also attached to the top. The response was processed in the frequency domain to obtain information on the concrete quality and length, but the test was only capable of providing results on a comparative basis among a group of piles. This method became more prevalent after the advent of digital signal processing, starting with the work of Rausche et al. [5, 6]. The method evolved over time and is currently referred to as the pulse-echo, sonic-echo, or impulse-response method [7-12].
Each of the above methods may have a bit different formulation but are based on the same basic idea. The procedures constitute impacting the top of the pile and recoding the response on the top using a transducer. Travel time and wave velocity of longitudinal waves are used to obtain the length of the foundation. The data analysis requires an experienced user, and the accuracy of the results are dependent on the assumed velocity of the wave and thus there can be significant error introduced even before considering the experimental uncertainties. Additionally, a modified version of this test exists which is similar to the test by Davis and Dunn, where the impact force is also measured during the test to obtain mobility plots from which the pile length is estimated. This modified test requires a bit more expensive equipment than the pulse echo method, yet it has all the limitations discussed pertaining to it. Most importantly, this method cannot be used whenever the top of the pile is inaccessible, and thus it is predominantly used for newly constructed foundations.
The other class of tests NDT of pile foundations are borehole techniques, including cross hole sonic logging, single hole sonic logging, gamma-gamma logging and parallel seismic testing [13], as well as induction testing for steel piles. All these tests require either a borehole alongside the pile foundation or a preinstalled test pipe in the pile and also require expensive equipment along with an experienced user to interpret the results. Even though these techniques can be effective in select situations, using them to test a large group of piles is not practical. Thus, there is still a need for a quick and effective techniques.
The idea of using lateral impact inducing flexural waves, rather than the conventional longitudinal waves from the impact-echo method, was apparently first conceived by Holt and Douglas [14]. Lateral impact imparts most energy into bending waves that are dispersive in nature. The analysis of dispersive waves is more complicated than non-dispersive waves such as longitudinal waves; unfortunately longitudinal waves are not well-excited due to lateral impact and it is essential to deal with dispersive flexural waves. Holt and Douglas introduced the Short-Kernel Method (SKM) to process the response from dispersive flexural waves to obtain the travel time information, which is used to estimate the embedded length of the pile. SKM consists of choosing a kernel of a particular frequency, generally the dominant frequency and obtaining a cross correlation between the kernel and the signal. The plot of the cross correlation is known as the short kernel plot. This plot contains information about that particular frequency (frequency of the kernel) from the signal and the time difference between consecutive peaks is used to obtain the velocity of wave propagation. Two wave trains are generated on impact, one upward propagating and one downward propagating. The first peak in the plot is when the downward propagating wave passes the accelerometer. The second peak is when the upward propagating wave gets reflected from the top and propagates downwards, reaching the accelerometer. The length from the top of the pile to the accelerometer is known and with the time of travel calculated from the first two peaks, the wave velocity is computed for the free part of the pile. This velocity obtained was used for the embedded part of the pile, along with the travel time calculated from the next peak to find the embedded length of the pile. A similar procedure was followed to calculate the wave velocity between two accelerometers, which was then used to calculate the embedded length using the time of travel for the reflected wave. This approach is completely based on the time of travel and does not take into account the effect of the soil and changes in wave velocity for the free and the embedded parts. Also the peak picking can be complicated even for an experienced user.
Another signal processing technique based on combined time-frequency analysis (Hilbert Huang Transforms) was used for the dispersive flexural waves by Farid [15]. Subhani et al. [16] used a combination of SKM and continuous wavelet transform (CWT), which is another time-frequency analysis technique, to estimate the embedded lengths of electricity poles and observed significant error margins in both the cases, up to 43% in some cases. The application of CWT is more straightforward than SKM, and SKM requires more experience with the user. The more recent work by Lo et al. [17] compares results from time, frequency and time-frequency analysis, but has been done for longitudinal waves. All the above methods are purely based on signal processing tools and do not explicitly incorporate the dispersion properties of the waves.